To find the number that should be subtracted from [tex]\(\frac{-3}{4}\)[/tex] to get [tex]\(\frac{5}{6}\)[/tex], we set up the following equation:
[tex]\[
\frac{-3}{4} - x = \frac{5}{6}
\][/tex]
Here, [tex]\(x\)[/tex] is the unknown number we need to determine. We can rearrange this equation to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-3}{4} - \frac{5}{6}
\][/tex]
To subtract these two fractions, we need a common denominator. The least common denominator (LCD) of 4 and 6 is 12. We convert both fractions to have this common denominator:
1. Convert [tex]\(\frac{-3}{4}\)[/tex] to a denominator of 12:
[tex]\[
\frac{-3}{4} = \frac{-3 \times 3}{4 \times 3} = \frac{-9}{12}
\][/tex]
2. Convert [tex]\(\frac{5}{6}\)[/tex] to a denominator of 12:
[tex]\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\][/tex]
Now we can subtract the fractions:
[tex]\[
x = \frac{-9}{12} - \frac{10}{12}
\][/tex]
Perform the subtraction of the numerators while keeping the denominator the same:
[tex]\[
x = \frac{-9 - 10}{12} = \frac{-19}{12}
\][/tex]
Therefore, the number that should be subtracted from [tex]\(\frac{-3}{4}\)[/tex] to get [tex]\(\frac{5}{6}\)[/tex] is:
[tex]\[
x = \frac{-19}{12}
\][/tex]
